The arm motions are controlled in end-effector space by a Cartesian impedance controller.
The time varying reference or attractor point of the end effector \(\mathbf {x}_d\)  is governed by a motion generator (MG).
Given the joint configuration \(\mathbf {q}\) , we can calculate the end-effector pose \(\mathbf {x}_{ee}\)  using forward kinematics and obtain an error term \(\mathbf {x}_e = \mathbf {x}_{ee} - \mathbf {x}_d\) .
Together with the joint velocities \(\dot{\mathbf {q}}\) , the Jacobian \(\mathbf {J}(\mathbf {q})\) , the configurable stiffness and damping matrices \(K_{d}\)  and \(D_{d}\) , the task control is formulated as
\(\mathbf {\tau }_{c}=\mathbf {J}^{T}(\mathbf {q})\left(-\mathbf {K}_{d} \mathbf {x}_{e}-\mathbf {D}_{d} \mathbf {J}(\mathbf {q}) \mathbf {\dot{q}}\right).\) 
Additionally, the task control can be overlayed with commanded generalized forces and torques \(\mathbf {F}_{ext}=\left(f_{x}~f_{y}~f_{z}~\tau _{x}~\tau _{y}~\tau _{z}\right)\) :
\(\mathbf {\tau }_{ext}=\mathbf {J}^{T}(\mathbf {q}) \mathbf {F}_{ext}.\) 
We utilize the integration introduced in [1]} and used in [2]}, which proposes to parameterize the MG with movement skills from the BT. The reference pose is shaped by 1) a linear trajectory to a goal point and 2) overlay motions that can be added to the reference pose as discussed in [1]}, [2]}. E.g. an Archimedes spiral for search.
